Limit state analysis of asymmetrical microstructures based on yield design computational homogenization approach

Abstract

This paper presents a novel formulation for the computational homogenization analysis of materials at the limit state. The polynomial interpolations are employed to impose the periodic boundary conditions for the fluctuating term of the displacement field when using arbitrary finite element meshes. Second-order cone programming provides an efficient solution to solve the resulting optimization problems, and accurate load multipliers can be obtained with the minimum computational cost. Several asymmetrical material models are investigated to perform the efficiency of the proposed method. The collapse mechanisms of the representative volume elements are also presented.